Let L be the straight line joining the points P(1, 2, –1) and Q(2, 3, 1). Let S be the foot of the perpendicular drawn from the point R(4, –1, 5) to the line L. Another line passing through R intersects L at a point T such that the point S divides the line segment PT internally in the ratio $|PS| : |ST| = 1 : 2$, where $|PS|$ and $|ST|$ are the lengths of the line segments PS and ST, respectively.

Then which of the following statements is (are) TRUE?

Let P be the plane such that it contains the straight line $\frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1}$ and is perpendicular to the plane $x+2y+3z=4$. Let $P_1$ be the plane which passes through the point $(4,2,2)$ and is parallel to P.

Then which of the following statements is (are) TRUE?

Let $L_1$ be the line of intersection of the planes given by the equations

$2x + 3y + z = 4$ and $x + 2y + z = 5$.

Let $L_2$ be the line passing through the point $P(2, -1, 3)$ and parallel to $L_1$. Let $M$ denote the plane given by the equation

$2x + y - 2z = 6$.

Suppose that the line $L_2$ meets the plane $M$ at the point $Q$. Let $R$ be the foot of the perpendicular drawn from $P$ to the plane $M$.

Then which of the following statements is (are) TRUE?